Question: Simplify the following expression: $q = \dfrac{t^2 - 2t - 35}{t - 7} $
Solution: First factor the polynomial in the numerator. $ t^2 - 2t - 35 = (t - 7)(t + 5) $ So we can rewrite the expression as: $q = \dfrac{(t - 7)(t + 5)}{t - 7} $ We can divide the numerator and denominator by $(t - 7)$ on condition that $t \neq 7$ Therefore $q = t + 5; t \neq 7$